Quarkonium Production at High-Energy Colliders

TL;DR

The paper assesses heavy quarkonium production at high-energy colliders through the NRQCD factorisation framework, emphasizing colour-octet mechanisms to explain large charmonium cross sections observed at the Tevatron and probing the universality of non-perturbative matrix elements. It highlights tensions between NRQCD predictions and observed polarisation at high pT, and discusses the sizable theoretical uncertainties stemming from higher-order QCD corrections and initial-state effects. The work surveys hadron and electron-proton collider data, contrasts with colour-evaporation models, and outlines crucial directions, including NLO calculations and kT-factorisation, to rigorously test NRQCD and its applicability to charmonium and bottomonium. Prospects for Tevatron Run II and the LHC, as well as the HERA upgrade, are presented as key opportunities to refine the theory and achieve a more complete understanding of quarkonium production.

Abstract

The theoretical description of heavy quarkonium production at high-energy p-pbar and e-p colliders is reviewed. Predictions based on non-relativistic QCD factorisation are confronted with recent charmonium and bottomonium data from the Tevatron and HERA. Potential shortcomings of the present theoretical analyses are discussed, and the prospects for quarkonium physics at the upgraded Tevatron and HERA colliders and at the LHC are summarised.

Figures (18)

• Figure 1: Generic diagrams for $J/\psi$ and $\psi(2S)$ production in hadron-hadron collisions through colour-singlet and colour-octet channels.
• Figure 2: Colour-singlet and colour-octet contributions to direct $J/\psi$ production in $p\bar{p} \to J/\psi+X$ at the Tevatron ($\sqrt{s}=1.8$ TeV, pseudorapidity cut $|\eta|<0.6$)) compared to experimental data from CDF Abe:1997jz. Parameters: CTEQ5L parton distribution functions Lai:1999wy; factorisation and renormalisation scale $\mu = \sqrt{p_t^2+4m_c^2}$; $m_c = 1.5$ GeV. The leading logarithms $(\alpha_s\ln p_t^2/(2m_c)^2)^n$ have been summed by solving the Altarelli-Parisi evolution equations for the gluon fragmentation function. NRQCD matrix elements as specified in Table \ref{['table1']}.
• Figure 3: Same as Figure \ref{['figure2']} for $\psi(2S)$ production.
• Figure 4: Same as Figure \ref{['figure2']} for $\chi_c$ production. Experimental data from Abe:1997yz.
• Figure 5: Polar angle asymmetry $\alpha$ for $\psi(2S)$ production in $p\bar{p} \to \psi(2S)(\to \mu^+\mu^-)+X$ at the Tevatron as a function of $p_t$ compared to experimental data from CDF Affolder:2000nn. Parameter specifications as in Figure \ref{['figure2']}. NLO corrections to the fragmentation contribution Beneke:1996ybBeneke:1997yw have been included. The error band is obtained as a combination of the uncertainty (statistical only) in the extraction of the NRQCD matrix elements [Table \ref{['table1']}] and the limiting cases that either $\langle {\cal O}^{\psi}[8,{}^1S_0]\rangle$ or $\langle {\cal O}^{\psi}[8,{}^3P_0]\rangle$ is set to zero in the linear combination extracted from the data.